Simplify the following expression: $\sqrt{99} + \sqrt{176}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{99} + \sqrt{176}$ $= \sqrt{9 \cdot 11} + \sqrt{16 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{11} + \sqrt{16} \cdot \sqrt{11}$ $= 3\sqrt{11} + 4\sqrt{11}$ Finally, simplify by combining the terms. $= ( 3 + 4 )\sqrt{11} = 7\sqrt{11}$